How to set Node's group color via Python?
A node group is also a node, so you set the node group's color the same way you do any other node:

import bpy
C = bpy.context
D = bpy.data

compTree = C.scene.node_tree                   # Compositing node tree
matTree  = D.materials['MyMaterial'].node_tree # 'MyMaterial' material node tree

t = compTree # For this example we'll use the compositing node tree

groupName = 'Group'

# Turn on custom color
t.nodes[ groupName ].use_custom_color = True

# Set group's color to pink
t.nodes[ groupName ].color = ( 0.5, 0.2, 0.75 )